Yes this is correct. There is no connection between animation space Perspective camera views and drawing perspective camera views.
The drawing view perspective is a little more angled than the design space perspective camera. Is this what bothers you?

One thing that might help you is using a Named View camera for the drawing. However this is a tricky workflow due to limitations in the Animation workspace.
Here's the trick:
1. Set up an animation view just like you'd like to see it in the drawing
2. Exit Animation and enter Design workspace
3. Immediately create a new Named View

When you create the drawing view, call up the custom camera.

Phil Eichmiller
Software Engineer
Quality Assurance
Autodesk, Inc.